Answer
$\dfrac{1}{x^3y^6}$
Work Step by Step
Recall:
(1) $a^{\frac{m}{n}}=\sqrt[n]{a^m}$
(2) $\left(a^m\right)^n=a^{mn}$
(3) $(ab)^m=a^mb^m$
(4) $a^{-m} = \dfrac{1}{a^m}$
Use rule (3) above to obtain:
\begin{align*}
&=\left(x^{\frac{1}{6}}\right)^{-18}\left(y^{\frac{1}{3}}\right)^{-18}
\end{align*}
Use rule (2) above to obtain:
\begin{align*}
&=x^{\frac{1}{6}(-18)} \cdot y^{\frac{1}{3}(-18)}\\\\
&=x^{-3} \cdot y^{-6}
\end{align*}
Use rule (4) above to obtain:
\begin{align*}
&=\dfrac{1}{x^3} \cdot \dfrac{1}{y^6}\\\\
&=\dfrac{1}{x^3y^6}
\end{align*}
